The main result of [1]} establishes Dirac cohomology as an invariant of \(\pi \) . And a natural problem relevant to the study of the unitary dual is: Can we classify all the irreducible unitary representations of \(G\)  with non-zero Dirac cohomology? Let us denote this set by \(\widehat{G}^d\) , and call it the Dirac series of \(G\)  (after J.-S. Huang). It is worth noting that when \(\pi \)  is unitary, \(\mathop {\hbox{Ker}}\nolimits D \cap {\rm Im}\, D=\lbrace 0\rbrace \)  and (REF ) simplifies as \(H_D(\pi )=\mathop {\hbox{Ker}}\nolimits D^2\) . Moreover, it is exactly the members of \(\widehat{G}\)  such that (REF ) becomes equality that consist of the Dirac series. Therefore, \(\widehat{G}^d\)  cuts out the extreme members of \(\widehat{G}\)  in the sense of Dirac inequality, and we expect the Dirac series to be interesting. For instance it contains the discrete series, \(A_{\mathfrak {q}}(\lambda )\)  modules in the good range. Moreover, Example 6.3 of [2]} suggests that Dirac series go beyond elliptic representations. Note that the latter have applications in endoscopy. In view of the research announcement by Barbasch and Pandžić [3]}, Dirac series should have application in the theory of automorphic forms as well.
